Rarita-Schwinger fields on nearly K\"{a}hler manifolds

TL;DR

This paper explores Rarita-Schwinger fields on 6-dimensional nearly Kähler manifolds, revealing their connection to harmonic 3-forms and analyzing deformations of Killing spinors through differential operator relationships.

Contribution

It establishes the equivalence between Rarita-Schwinger fields and harmonic 3-forms and links infinitesimal deformations of Killing spinors to Laplace operator eigenspaces.

Findings

Rarita-Schwinger fields coincide with harmonic 3-forms.

Deformations of Killing spinors relate to Laplace eigenspaces.

Differential operator relationships clarify geometric structures.

Abstract

We study Rarita-Schwinger fields on 6-dimensional compact strict nearly K\"{a}hler manifolds. In order to investigate them, we clarify the relationship between some differential operators for the Hermitian connection and the Levi-Civita connection. As a result, we show that the space of the Rarita-Schwinger fields coincides with the space of the harmonic 3-forms. Applying the same technique to a deformation theory, we also find that the space of the infinitesimal deformations of Killing spinors coincides with the direct sum of a certain eigenspace of the Laplace operator and the space of the Killing spinors.